Method for transmitting data in mulitiple antenna system

ABSTRACT

A method of sending data in a multiple antenna system includes the steps of generating a transmission signal by applying channel-dependent precoding to a first antenna cluster and a second antenna cluster, each comprising a plurality of antennas, wherein the channel-dependent precoding is performed by a precoding weight matrix in which a precoding weight for each of the antenna clusters has a block diagonal form and the precoding weight is represented by P×V for a number of transmission antennas P, included in each of the antenna clusters, and a number of layers V applied to each of the antenna clusters (P and V are an integer greater than 0) and sending the transmission signal.

TECHNICAL FIELD

The present invention relates to wireless communication, and morespecifically to a method of sending data using multiple antennas.

BACKGROUND ART

A Multiple-Input Multiple-Output (MIMO) has recently been in thespotlight in order to maximize the performance and communicationcapacity of a wireless communication system. MIMO technology is a methodwhich breaks away from technology using one transmission antenna and onereception antenna and can improve the transmission efficiency oftransmission/reception data by adopting multiple transmission antennasand multiple reception antennas. An MIMO system is also called amultiple antenna system. MIMO technology is the application oftechnology for gathering and completing data pieces received by severalantennas without being dependent on a single antenna path in order toreceive one entire message. Consequently, the data transfer rate may beimproved in a specific range or the range of a system for a specificdata transfer rate may be increased.

MIMO technology includes a transmission diversity, spatial multiplexing,beamforming, and so on. The transmission diversity is technology forsending the same data through multiple transmission antennas in order toincrease transmission reliability. The spatial multiplexing istechnology for sending data at high speed without increasing thebandwidth of a system by sending different data through multipletransmission antennas at the same time. The beamforming is used toincrease the Signal to Interference plus Noise Ratio (SINR) of a signalby applying a weight according to a channel state in multiple antennas.The weight may be represented by a weight vector or a weight matrix andcalled a precoding vector or a precoding matrix.

The spatial multiplexing includes spatial multiplexing for a single userand spatial multiplexing for multiple users. The spatial multiplexingfor a single user is called a Single User MIMO (SU-MIMO), and thespatial multiplexing for multiple users is called Spatial DivisionMultiple Access (SDMA) or a Multi-User MIMO (MU-MIMO). The capacity ofan MIMO channel is increased in proportion to the number of antennas. AnMIMO channel may be divided into independent channels. Assuming that thenumber of transmission antennas is Nt and the number of receptionantennas is Nr, the number of independent channels Ni is Ni≦min{Nt, Nr}.Each of the independent channels may be said to be a spatial layer. Arank is the number of non-zero eigenvalues of an MIMO channel matrix andmay be defined as the number of spatial streams that can be multiplexed.

MIMO technology includes a codebook-based precoding scheme. Thecodebook-based precoding scheme is a method of selecting a precodingmatrix which is the most similar to an MIMO channel, from amongpredetermined precoding matrices, and sending a Precoding Matrix Index(PMI). This method can reduce the overhead of feedback data. A codebookconsists of codebook sets which can represent spatial channels. In orderto increase the data transfer rate, the number of antennas has to beincreased. With an increase of the number of antennas, a codebook has toconsist of a more number of codebook sets. If the number of codebooksets increases according to the increased number of antennas, not onlythe overhead of feedback data may be increased, but also there is adifficulty in designing the codebook.

There is a need for a method to which a codebook-based precoding schemecan be efficiently applied in a multiple antenna system having anincreased number of antennas as compared with the existing number ofantennas.

DISCLOSURE Technical Problem

An object to be achieved by the present invention is to provide a methodcapable of efficiently applying a codebook-based precoding scheme tomultiple increased antennas.

Technical Solution

A method of sending data in a multiple antenna system according to anaspect of the present invention includes the steps of generating atransmission signal by applying channel-dependent precoding to a firstantenna cluster and a second antenna cluster, each comprising aplurality of antennas, wherein the channel-dependent precoding isperformed by a precoding weight matrix in which a precoding weight foreach of the antenna clusters has a block diagonal form and the precodingweight is represented by P×V for a number of transmission antennas P,included in each of the antenna clusters, and a number of layers Vapplied to each of the antenna clusters (P and V are an integer greaterthan 0) and sending the transmission signal.

A method of a User Equipment (UE) operating in a multiple antenna systemaccording to another aspect of the present invention includes the stepsof estimating a plurality of transmission antenna channels of a BaseStation (BS), feeding a channel-dependent precoding matrix or aPrecoding Matrix Index (PMI) for a first cluster and a second cluster,comprising a plurality of different antennas, from the estimatedchannels to the BS, and receiving precoded and transmitted data usingthe feedback precoding matrix or a precoding weight induced from the PMIor directly used.

Advantageous Effects

The existing codebook can be utilized with respect to multiple antennasmore increased than the antennas of the existing multiple antennasystem. Accordingly, the complexity of a system can be reduced, andbackward compatibility for a user equipment not supporting multipleincreased antennas can be guaranteed.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram showing a wireless communication system;

FIG. 2 shows an example of a transmitter structure;

FIG. 3 shows data processing between a transmitter and a receiver in amultiple antenna system; and

FIG. 4 shows antenna clustering according to an embodiment of thepresent invention.

MODE FOR INVENTION

FIG. 1 is a block diagram showing a wireless communication system. Thewireless communication systems are widely deployed in order to providevarious communication services, such as voice and packet data.

Referring to FIG. 1, the wireless communication system includes UserEquipment (UE) 10 and a Base Station (BS) 20. The UE 10 may be fixed ormobile and called another terminology, such as a Mobile Station (MS), aUser Terminal (UT), a Subscriber Station (SS), or a wireless device. Ingeneral, the BS 20 refers to a fixed station communicating with the UEs10, and it may be called another terminology, such as a Node-B, a BaseTransceiver System (BTS), or an access point. One or more cells mayexist in one BS 20.

Hereinafter, downlink (DL) refers to communication from the BS 20 to theUE 10, and uplink (UL) refers to communication from the UE 10 to the BS20. In downlink, a transmitter may be part of the BS 20, and a receivermay be part of the UE 10. In uplink, a transmitter may be part of the UE10, and a receiver may be part of the BS 20.

The wireless communication system may be an Orthogonal FrequencyDivision Multiplexing (OFDM)/Orthogonal Frequency Division MultipleAccess (OFDMA)-based system. OFDM employs a plurality of orthogonalsubcarriers. OFDM employs an orthogonality characteristic betweenInverse Fast Fourier Transform (IFFT) and Fast Fourier Transform (FFT).A transmitter performs IFFT on data and sends the data. A receiverrestores original data by performing FFT on a reception signal. Thetransmitter uses IFFT in order to combine multiple subcarriers, and thereceiver uses corresponding FFT in order to separate multiplesubcarriers.

The wireless communication system may be a multiple antenna system.

The multiple antenna system may be a Multiple-Input Multiple-Output(MIMO) system. Alternatively, the multiple antenna system may be aMultiple-Input Single-Output (MISO) system, a Single-Input Single-Output(SISO) system, or a Single-Input Multiple-Output (SIMO) system. The MIMOsystem uses a plurality of transmission antennas and a plurality ofreception antennas. The MISO system uses a plurality of transmissionantenna and one reception antenna. The SISO system uses one transmissionantenna and one reception antenna. The SIMO system uses one transmissionantenna and a plurality of reception antenna.

In the multiple antenna system, Space-Time Coding (SPC), such as SpaceFrequency Block Codes (SFBC) and Space Time Block Codes (STBC), CyclicDelay Diversity (CDD), Frequency Switched Transmit Diversity (FSTD), andTime Switched Transmit Diversity (TSTD) may be used as a scheme usingmultiple antennas at rank 1. Spatial Multiplexing (SM), GeneralizedCyclic Delay Diversity (GCDD), and Selective Virtual Antenna Permutation(S-VAP) may be used as a scheme using multiple antennas at rank 2 orhigher. SFBC is a scheme capable of securing both a diversity gain and amultiple user scheduling gain in a corresponding dimension byefficiently applying selectivity in the space region and the frequencydomain. STBC is a scheme for applying selectivity in the space regionand the time domain. FSTD is a scheme for classifying signals,transmitted through multiple antennas, according to frequencies. TSTD isa scheme for classifying signals, transmitted through multiple antennas,according to time. Spatial multiplexing is a scheme for raising thetransmission rate by sending different data per antenna. GCDD is ascheme for selectivity in the time domain and the frequency domain.S-VAP is a scheme using a single precoding matrix, and it includes aMulti Codeword (MCW) S-VAP in which multiple codewords are mixed betweenantennas in spatial diversity or spatial multiplexing and a SingleCodeword (SCVV) S-VAP using a single codeword.

FIG. 2 shows an example of a transmitter structure.

Referring to FIG. 2, the transmitter 100 includes encoders 110-1 to110-K, modulators 120-1 to 120-K, a layer mapper 130, a precoder 140,subcarrier mappers 150-1 to 150-K, and OFDM signal generators 160-1 to160-K. The transmitter 100 includes an Nt (Nt≧1) number of transmissionantennas 170-1 to 170-Nt.

The encoders 110-1 to 110-K form coded data by encoding received dataaccording to a predetermined coding scheme. The coded data may be calleda codeword, and a codeword b may be represented by Equation 1 below.

b^((q))(0), . . . , b^((q))(M _(bit) ^((q))−1)   [Equation 1]

wherein q is the index of a codeword, and M_(bit) ^((q)) is the numberof bits of the codeword q.

The codeword is subjected to scrambling. A scrambled codeword c may berepresented by Equation 2.

c^((q))(0), . . . , c^((q))(M_(bit) ^((q))−1)   [Equation 2]

The modulators 120-1 to 120-K arrange the codeword in the form ofsymbols which represent locations on a signal constellation. Themodulation scheme is not limited and may be m-Phase Shift Keying (m-PSK)or m-Quadrature Amplitude Modulation (m-QAM). For example, the m-PSK maybe BPSK, QPSK, or 8-PSK, and the m-QAM may be 16-QAM, 64-QAM, or256-QAM.

The codeword d arranged in the form of the symbols on the signalconstellation may be represented by Equation 3.

d^((q))(0), . . . , d^((q))(M_(symb) ^((q))−1)   [Equation 3]

wherein M_(symb) ^((q)) is the number of symbol of the codeword q.

The layer mapper 130 defines the layer of an input symbol such that theprecoder 140 can distribute antenna-specific symbols to the path of eachantenna. The layer is defined as information path to the precoder 140. Asymbol x inputted to the path of each antenna may be represented byEquation 4.

x(i)=[x ⁽⁰⁾(i) . . . x ^((υ−1))(i)]^(T)   [Equation 4]

wherein υ indicates the number of layers.

Information path anterior to the precoder 140 may be called a virtualantenna or layer. The precoder 140 processes the input symbols accordingto the MIMO scheme according to the multiple transmission antennas 170-1to 170-Nt. For example, the precoder 140 may use codebook-basedprecoding. The precoder 140 distributes the antenna-specific symbolsinto the subcarrier mappers 150-1 to 150-K of the path of acorresponding antenna. Each piece of information path transmitted fromthe precoder 140 to one antenna through one subcarrier mapper is calleda stream. This may be called a physical antenna.

A signal y^((p))(i) sent to each antenna port p may be represented byEquation 5.

y(i)=[ . . . y ^(9p))(i) . . . ]^(T)   [Equation 5]

The subcarrier mappers 150-1 to 150-K allocate the input symbols toproper subcarriers and multiplex the input symbols according to a user.The OFDM signal generators 160-1 to 160-K modulate the input symbolsaccording to an OFDM scheme and output OFDM symbols. The OFDM signalgenerators 160-1 to 160-K may perform IFFT (Inverse Fast FourierTransform) on the input symbols, and a Cyclic Prefix (CP) may beinserted into a time domain symbol on which IFFT has been performed. TheOFDM symbols are transmitted through the respective transmissionantennas 170-1 to 170-Nt.

In the MIMO system, the transmitter 100 may be operated in two kinds ofmodes. One of the two kinds of modes is an SCW mode, and the otherthereof is an MCW mode. In the SCW mode, transmission signalstransmitted through MIMO channels have the same data rate. In the MCWmode, data transmitted through MIMO channels may be independently coded,and transmission signals may have different data rates. The MCW mode isoperated when the rank is 2 or higher.

FIG. 3 shows data processing between a transmitter and a receiver in amultiple antenna system.

Referring to FIG. 3, the transmitter 200 includes a scheduler 210, achannel encoder/mapper 220, an MIMO encoder 230, and an OFDM modulator240. The transmitter 200 includes an Nt (Nt>1) number of transmissionantennas. The transmitter 200 may be part of a BS in downlink and may bepart of a UE in uplink.

The scheduler 210 receives data from an N number of users and outputs aK number of streams to be transmitted at once. The scheduler 210determines a user to which available radio resources will be transmittedand the transmission rate on the basis of channel information of eachuser. The scheduler 210 extracts channel information from feedback dataand selects a code rate, a Modulation and Coding Scheme (MCS) and so on.For the operation of an MIMO system, the feedback data may includepieces of control information, such as a Channel Quality Indicator(CQI), Channel State Information (CSI), a channel covariance matrix, aprecoding weight, and a channel rank. The CSI includes a channel matrix,a channel correlation matrix, a quantized channel matrix, or a quantizedchannel correlation matrix between a transmitter and a receiver. The CQIincludes a Signal to Noise Ratio (SNR), a Signal to Interference andNoise Ratio (SINR), etc. between a transmitter and a receiver.

Available radio resources allocated by the scheduler indicate radioresources used when data is transmitted in a wireless communicationsystem. For example, in a Time Division Multiple Access (TDMA) system,each time slot is resources. In a Code Division Multiple Access (CDMA)system, each code and each time slot are resources. In an OrthogonalFrequency Division Multiple Access (OFDMA) system, each subcarrier andeach time slot are resources. In order not to cause interference withother users within the same cell or sector, each resource may beorthogonally defined in the time, code, or frequency domain.

The channel encoder/mapper 220 forms coded data by encoding receivedstreams according to a predetermined coding scheme and maps the codeddata to symbols which represent locations on a signal constellation. TheMIMO encoder 230 performs precoding on the received symbols. Suchprecoding is a scheme for preprocessing symbols to be transmitted. Theprecoding scheme includes RBF (random beamforming), ZFBF (zero forcingbeamforming), etc. which generate symbols using a weight vector or aprecoding matrix. Codebook-based precoding using predetermined codebooksets may be used as the precoding scheme.

The OFDM modulator 240 allocates the received symbols to propersubcarriers and sends the subcarriers through the transmission antennas.

The receiver 300 includes an OFDM demodulator 310, a channel estimator320, an MIMO decoder 330, a channel decoder/demapper 340, and a feedbackinformation acquisition unit 350. The receiver 300 includes an Nr (Nr>1)number of reception antennas. The receiver 300 may be part of a UE indownlink and part of a BS in uplink.

Signals received from the reception antennas are demodulated by the OFDMdemodulator 310. The channel estimator 320 estimates channels. The MIMOdecoder 330 performs post processing corresponding to the MIMO encoder230. The decoder/demapper 340 demaps the received symbols into codeddata and restores original data by decoding the coded data. The feedbackinformation acquisition unit 350 generates user information 360,including CSI, CQI, a PMI, and so on. The generated user information 360is composed of feedback data and transmitted to the transmitter 200.

’Feedback Data of an MIMO-OFDM System>

For the operation of an MIMO-OFDM system, pieces of control information,such as a CQI, CSI, a channel covariance matrix, a precoding weight, anda channel rank, are required. In a Frequency Division Duplex (FDD)system, a receiver reports the pieces of information through feedbackchannels. In a Time Division Duplex (TDD) system, pieces of informationto be used for downlink transmission may be acquired by estimatinguplink channels using the reciprocity characteristic of a channel.

The CQI is necessary for the allocation of resources and linkadaptation. An SNR, an SINR, etc. may be used as the CQI. The SNR/SINRmay be quantized in 16 levels of a 1.89dB interval and defined as a4-bit CQI. The receiver quantizes the SNR/SINR and reports a defined CQIindex to the transmitter. Furthermore, when an MIMO scheme is used, amaximum of 2 codewords (CVV) may be supported. That is, for rank 2 orhigher transmission, the CQIs of a first CW and a second CW have to bereported to the transmitter. The first CW may be represented by 4 bits,and the second CW may be represented by 3 bits as a difference with thefirst CW.

The precoding scheme is an MIMO scheme for preprocessing and sendingtransmission data strings using a preprocessing weight. Equation 6represents a precoding scheme for preprocessing a transmission datastring x using a preprocessing weight.

$\begin{matrix}{{\begin{bmatrix}{y^{(0)}(i)} \\\vdots \\{y^{({P - 1})}(i)}\end{bmatrix} = {{W(i)}\begin{bmatrix}{x^{(0)}(i)} \\\vdots \\{x^{({v - 1})}(i)}\end{bmatrix}}}{{where},{i = 0},1,{\ldots \mspace{14mu} M_{symb}^{layer}}}} & \left\lbrack {{Equation}\mspace{14mu} 6} \right\rbrack\end{matrix}$

wherein W(i) indicates a precoding matrix. A preprocessed transmissiondata string y may employ a diversity matrix D(i) and a DFT matrix U forCyclic Delay Diversity (CDD) as in Equation 7.

$\begin{matrix}{\begin{bmatrix}{y^{(0)}(i)} \\\vdots \\{y^{({P - 1})}(i)}\end{bmatrix} = {{W(i)}{D(i)}{U\begin{bmatrix}{x^{(0)}(i)} \\\vdots \\{x^{({\upsilon - 1})}(i)}\end{bmatrix}}}} & \left\lbrack {{Equation}\mspace{14mu} 7} \right\rbrack\end{matrix}$

D(i) and U may be determined according to a transmission layer.

Equation 8 shows an example in which a precoding matrix W(i) accordingto the rank is generated.

$\begin{matrix}{{{W(i)} = C_{k}}{{k = {\left( {\left\lfloor \frac{i}{\upsilon} \right\rfloor {mod}\; 4} \right) + 1}},{where}}{{k = 1},2,3,4,}} & \left\lbrack {{Equation}\mspace{14mu} 8} \right\rbrack\end{matrix}$

wherein C1, C2, C3, and C4 indicate precoding matrices corresponding torespective precoder indices 12, 13, 14, and 15. υ indicates a rank(transmission layer).

Table 1 shows an example of a delay matrix D(i) and a DFT matrix U forCDD (cyclic delay diversity) which is applied according to thetransmission layer.

TABLE 1 Number of layers υ U D(i) 2 $\frac{1}{\sqrt{2}}\begin{bmatrix}1 & 1 \\1 & {e\text{?}}\end{bmatrix}$ ?indicates text missing or illegible when filed$\begin{bmatrix}1 & 0 \\0 & {e\text{?}}\end{bmatrix}$ ?indicates text missing or illegible when filed 3$\frac{1}{\sqrt{3}}\begin{bmatrix}1 & 1 & 1 \\1 & {e\text{?}} & {e\text{?}} \\1 & {e\text{?}} & {e\text{?}}\end{bmatrix}$ ?indicates text missing or illegible when filed$\begin{bmatrix}1 & 0 & 0 \\0 & {e\text{?}} & 0 \\0 & 0 & {e\text{?}}\end{bmatrix}$ ?indicates text missing or illegible when filed 4$\frac{1}{2}\begin{bmatrix}1 & 1 & 1 & 1 \\1 & {e\text{?}} & {e\text{?}} & {e\text{?}} \\1 & {e\text{?}} & {e\text{?}} & {e\text{?}} \\1 & {e\text{?}} & {e\text{?}} & {e\text{?}}\end{bmatrix}$ ?indicates text missing or illegible when filed$\begin{bmatrix}1 & 0 & 0 \\0 & {e\text{?}} & 0 \\0 & 0 & {e\text{?}}\end{bmatrix}$ ?indicates text missing or illegible when filed ??indicates text missing or illegible when filed

There are zero forcing beamforming, eigen beamforming, andcodebook-based precoding according to a method of generating theprecoding weight. In order to apply each of the schemes, a CSI, achannel covariance matrix, a codebook index, etc. are required. In theexisting system, codebook-based precoding is supported in two antennas(2Tx) and four antenna (4Tx) MIMO transmission. To this end, codebooksfor 2Tx/4Tx are defined.

In the codebook-based precoding scheme, a receiver has severalpredetermined precoding matrices, estimates channels using a signalreceived from a transmitter, and determines a precoding matrix which isthe most similar to an estimated channel state. The receiver feeds adetermined PMI back to the transmitter. The transmitter selects acodebook suitable for the feedback precoding matrix and sends data. Inthe codebook-based precoding scheme, the amount of the feedback data isgreatly reduced because only the PMI is transmitted. The codebook-basedprecoding scheme has a different system performance according to amethod of configuring a codebook, the type of the codebook, and the sizeof the codebook. In the codebook-based precoding scheme, if a codebookdoes not sufficiently represent a channel state, performance may bedeteriorated. However, if the size of a codebook is increased, thecodebook can sufficiently represent a channel state and thus mayapproach optimal performance. Accordingly, there is a need for a designof a codebook which can approach optimal performance while sufficientlyreducing the amount of feedback data.

With an increase of the number of transmission antennas, the size of arequired codebook is increased. In 2Tx transmission of the existingsystem, a codebook having four precoding matrices for a rank 1 and acodebook having three precoding matrices for a rank 2 are defined. In4Tx transmission of the existing system, a codebook having 16 precodingmatrices for each of ranks 1 to 4 is defined. Table 2 shows an exampleof a codebook for 4Tx MIMO.

TABLE 2 Codebook Number of Layers Index 1 2

3 4 0 $\begin{bmatrix}1 \\1 \\1 \\1\end{bmatrix}\quad$ $\frac{1}{\sqrt{2}}\begin{bmatrix}1 & 1 \\1 & {- 1} \\1 & {- 1} \\1 & 1\end{bmatrix}$ $\frac{1}{\sqrt{3}}\begin{bmatrix}1 & 1 & 1 \\1 & 1 & {- 1} \\1 & {- 1} & {- 1} \\1 & {- 1} & 1\end{bmatrix}$ $\frac{1}{\sqrt{4}}\begin{bmatrix}1 & 1 & 1 & 1 \\1 & 1 & {- 1} & {- 1} \\1 & {- 1} & 1 & {- 1} \\1 & {- 1} & {- 1} & 1\end{bmatrix}$ 1 $\begin{bmatrix}1 \\{- j} \\{- 1} \\j\end{bmatrix}\quad$ $\frac{1}{\sqrt{2}}\begin{bmatrix}1 & j \\{- j} & 1 \\{- 1} & j \\j & 1\end{bmatrix}$ $\frac{1}{\sqrt{3}}\begin{bmatrix}1 & j & {- 1} \\{- j} & 1 & {- j} \\{- 1} & j & 1 \\j & 1 & j\end{bmatrix}$ $\frac{1}{\sqrt{4}}\begin{bmatrix}1 & j & {- 1} & {- j} \\{- j} & 1 & {- j} & 1 \\{- 1} & j & 1 & {- j} \\j & 1 & j & 1\end{bmatrix}$ 2 $\begin{bmatrix}1 \\{- 1} \\1 \\{- 1}\end{bmatrix}\quad$ $\frac{1}{\sqrt{2}}\begin{bmatrix}1 & {- 1} \\{- 1} & 1 \\1 & 1 \\{- 1} & {- 1}\end{bmatrix}$ $\frac{1}{\sqrt{3}}\begin{bmatrix}1 & {- 1} & 1 \\{- 1} & 1 & 1 \\1 & 1 & 1 \\{- 1} & {- 1} & 1\end{bmatrix}$ $\frac{1}{\sqrt{4}}\begin{bmatrix}1 & {- 1} & 1 & {- 1} \\{- 1} & 1 & 1 & {- 1} \\1 & 1 & 1 & 1 \\{- 1} & {- 1} & 1 & 1\end{bmatrix}$ 3 $\begin{bmatrix}1 \\j \\{- 1} \\{- j}\end{bmatrix}\quad$ $\frac{1}{\sqrt{2}}\begin{bmatrix}1 & {- j} \\j & 1 \\{- 1} & {- j} \\{- j} & 1\end{bmatrix}$ $\frac{1}{\sqrt{3}}\begin{bmatrix}1 & {- j} & {- 1} \\j & 1 & j \\{- 1} & {- j} & 1 \\{- j} & 1 & {- j}\end{bmatrix}$ $\frac{1}{\sqrt{4}}\begin{bmatrix}1 & {- j} & {- 1} & j \\j & 1 & j & 1 \\{- 1} & {- j} & 1 & j \\{- j} & 1 & {- j} & 1\end{bmatrix}$ 4 $\begin{bmatrix}1 \\\frac{1 - j}{\sqrt{2}} \\{- j} \\\frac{{- 1} - j}{\sqrt{2}}\end{bmatrix}\quad$ $\frac{1}{\sqrt{2}}\begin{bmatrix}1 & \frac{{- 1} + j}{\sqrt{2}} \\\frac{1 - j}{\sqrt{2}} & {- j} \\{- j} & \frac{{- 1} - j}{\sqrt{2}} \\\frac{{- 1} - j}{\sqrt{2}} & 1\end{bmatrix}$ $\frac{1}{\sqrt{3}}\begin{bmatrix}1 & \frac{1 + j}{\sqrt{2}} & \frac{{- 1} + j}{\sqrt{2}} \\\frac{1 - j}{\sqrt{2}} & 1 & {- j} \\{- j} & \frac{{- 1} + j}{\sqrt{2}} & \frac{{- 1} - j}{\sqrt{2}} \\\frac{{- 1} - j}{\sqrt{2}} & j & 1\end{bmatrix}$ $\frac{1}{\sqrt{4}}\begin{bmatrix}1 & \frac{1 + j}{\sqrt{2}} & j & \frac{{- 1} + j}{\sqrt{2}} \\\frac{1 - j}{\sqrt{2}} & 1 & \frac{{- 1} - j}{\sqrt{2}} & {- j} \\{- j} & \frac{{- 1} + j}{\sqrt{2}} & 1 & \frac{{- 1} - j}{\sqrt{2}} \\\frac{{- 1} - j}{\sqrt{2}} & j & \frac{{- 1} + j}{\sqrt{2}} & 1\end{bmatrix}$ 5 $\frac{\begin{matrix}1 \\{{- 1}\text{?}j}\end{matrix}}{\sqrt{2}}$ $\frac{\begin{matrix}j \\{1 - j}\end{matrix}}{\sqrt{2}}$?indicates text missing or illegible when filed$\frac{1}{\sqrt{2}}\begin{bmatrix}1 & \frac{1 + j}{\sqrt{2}} \\\frac{{- 1} - j}{\sqrt{2}} & j \\j & \frac{1 - j}{\sqrt{2}} \\\frac{1 - j}{\sqrt{2}} & 1\end{bmatrix}$ $\frac{1}{\sqrt{3}}\begin{bmatrix}1 & \frac{{- 1} + j}{\sqrt{2}} & \frac{1 + j}{\sqrt{2}} \\\frac{{- 1} - j}{\sqrt{2}} & 1 & j \\j & \frac{1 + j}{\sqrt{2}} & \frac{1 - j}{\sqrt{2}} \\\frac{1 - j}{\sqrt{2}} & {- j} & 1\end{bmatrix}$ $\frac{1}{\sqrt{4}}\begin{bmatrix}1 & \frac{{- 1} + j}{\sqrt{2}} & {- j} & \frac{1 + j}{\sqrt{2}} \\\frac{{- 1} - j}{\sqrt{2}} & 1 & \frac{1 - j}{\sqrt{2}} & j \\j & \frac{1 + j}{\sqrt{2}} & 1 & \frac{1 - j}{\sqrt{2}} \\\frac{1 - j}{\sqrt{2}} & {- j} & \frac{1 + j}{\sqrt{2}} & 1\end{bmatrix}$ 6 $\begin{bmatrix}1 \\\frac{{- 1} + j}{\sqrt{2}} \\{- j} \\\frac{1 + j}{\sqrt{2}}\end{bmatrix}\quad$ $\frac{1}{\sqrt{2}}\begin{bmatrix}1 & j \\\frac{{- 1} + j}{\sqrt{2}} & \frac{1 + j}{\sqrt{2}} \\{- j} & 1 \\\frac{1 + j}{\sqrt{2}} & \frac{1 - j}{\sqrt{2}}\end{bmatrix}$ $\frac{1}{\sqrt{3}}\begin{bmatrix}1 & j & \frac{1 - j}{\sqrt{2}} \\\frac{{- 1} + j}{\sqrt{2}} & \frac{1 + j}{\sqrt{2}} & {- j} \\{- j} & 1 & \frac{1 + j}{\sqrt{2}} \\\frac{1 + j}{\sqrt{2}} & \frac{1 - j}{\sqrt{2}} & 1\end{bmatrix}$ $\frac{1}{\sqrt{4}}\begin{bmatrix}1 & \frac{{- 1} - j}{\sqrt{2}} & j & \frac{1 - j}{\sqrt{2}} \\\frac{{- 1} + j}{\sqrt{2}} & 1 & \frac{1 + j}{\sqrt{2}} & {- j} \\{- j} & \frac{1 - j}{\sqrt{2}} & 1 & \frac{1 + j}{\sqrt{2}} \\\frac{1 + j}{\sqrt{2}} & j & \frac{1 - j}{\sqrt{2}} & 1\end{bmatrix}$ 7 $\begin{bmatrix}1 \\\frac{1 + j}{\sqrt{2}} \\j \\\frac{{- 1} + j}{\sqrt{2}}\end{bmatrix}\quad$ $\frac{1}{\sqrt{2}}\begin{bmatrix}\frac{\begin{matrix}1 \\{1 + j}\end{matrix}}{\text{?}} & \frac{\begin{matrix}{- j} \\{{- 1} + j}\end{matrix}}{\text{?}} \\\frac{\begin{matrix}j \\{{- 1} - j}\end{matrix}}{\text{?}} & \frac{\begin{matrix}1 \\{{- 1} - j}\end{matrix}}{\text{?}}\end{bmatrix}$ ?indicates text missing or illegible when filed$\frac{1}{\sqrt{3}}\begin{bmatrix}1 & {- j} & \frac{{- 1} - j}{\sqrt{2}} \\\frac{1 + j}{\sqrt{2}} & \frac{{- 1} + j}{\sqrt{2}} & j \\j & 1 & \frac{{- 1} + j}{\sqrt{2}} \\\frac{{- 1} + j}{\sqrt{2}} & \frac{{- 1} - j}{\sqrt{2}} & 1\end{bmatrix}$ $\frac{1}{\sqrt{4}}\begin{bmatrix}1 & \frac{1 - j}{\sqrt{2}} & {- j} & \frac{{- 1} - j}{\sqrt{2}} \\\frac{1 + j}{\sqrt{2}} & 1 & \frac{{- 1} + j}{\sqrt{2}} & j \\j & \frac{{- 1} - j}{\sqrt{2}} & 1 & \frac{{- 1} + j}{\sqrt{2}} \\\frac{{- 1} - j}{\sqrt{2}} & {- j} & \frac{{- 1} - j}{\sqrt{2}} & 1\end{bmatrix}$ 8 $\begin{bmatrix}1 \\1 \\{- 1} \\{- 1}\end{bmatrix}\quad$ $\frac{1}{\sqrt{2}}\begin{bmatrix}1 & 1 \\1 & 1 \\{- 1} & 1 \\{- 1} & 1\end{bmatrix}$ $\frac{1}{\sqrt{3}}\begin{bmatrix}1 & 1 & {- 1} \\1 & 1 & 1 \\{- 1} & 1 & {- 1} \\{- 1} & 1 & 1\end{bmatrix}$ $\frac{1}{\sqrt{4}}\begin{bmatrix}1 & 1 & {- 1} & {- 1} \\1 & 1 & 1 & 1 \\{- 1} & 1 & 1 & {- 1} \\{- 1} & 1 & {- 1} & 1\end{bmatrix}$ 9 $\begin{bmatrix}1 \\{- j} \\1 \\{- j}\end{bmatrix}\quad$ $\frac{1}{\sqrt{2}}\begin{bmatrix}1 & j \\{- j} & {- 1} \\1 & {- j} \\{- j} & 1\end{bmatrix}$ $\frac{1}{\sqrt{3}}\begin{bmatrix}1 & 1 & j \\{- j} & j & {- 1} \\1 & 1 & {- j} \\{- j} & j & 1\end{bmatrix}$ $\frac{1}{\sqrt{4}}\begin{bmatrix}1 & j & 1 & j \\{- j} & 1 & j & {- 1} \\1 & {- j} & 1 & {- j} \\{- j} & {- 1} & j & 1\end{bmatrix}$ 10 $\begin{bmatrix}1 \\{- 1} \\{- 1} \\1\end{bmatrix}\quad$ $\frac{1}{\sqrt{2}}\begin{bmatrix}1 & {- 1} \\{- 1} & {- 1} \\{- 1} & 1 \\1 & 1\end{bmatrix}$ $\frac{1}{\sqrt{3}}\begin{bmatrix}1 & {- 1} & {- 1} \\{- 1} & 1 & {- 1} \\{- 1} & {- 1} & 1 \\1 & 1 & 1\end{bmatrix}$ $\frac{1}{\sqrt{4}}\begin{bmatrix}1 & {- 1} & {- 1} & 1 \\{- 1} & 1 & {- 1} & 1 \\{- 1} & {- 1} & 1 & 1 \\1 & 1 & 1 & 1\end{bmatrix}$ 11 $\begin{bmatrix}1 \\j \\1 \\j\end{bmatrix}\quad$ $\frac{1}{\sqrt{2}}\begin{bmatrix}1 & 1 \\j & {- j} \\1 & 1 \\j & {- j}\end{bmatrix}$ $\frac{1}{\sqrt{3}}\begin{bmatrix}1 & 1 & {- j} \\j & {- j} & {- 1} \\1 & 1 & j \\j & {- j} & 1\end{bmatrix}$ $\frac{1}{\sqrt{4}}\begin{bmatrix}1 & {- j} & 1 & {- j} \\j & 1 & {- j} & {- 1} \\1 & j & 1 & j \\j & {- 1} & {- j} & 1\end{bmatrix}$ 12 $\begin{bmatrix}1 \\1 \\1 \\{- 1}\end{bmatrix}\quad$ $\frac{1}{\sqrt{2}}\begin{bmatrix}1 & 1 \\1 & 1 \\1 & {- 1} \\{- 1} & 1\end{bmatrix}$ $\frac{1}{\sqrt{3}}\begin{bmatrix}1 & 1 & 1 \\1 & 1 & {- 1} \\1 & {- 1} & 1 \\{- 1} & 1 & 1\end{bmatrix}$ $\frac{1}{\sqrt{4}}\begin{bmatrix}1 & 1 & 1 & {- 1} \\1 & 1 & {- 1} & 1 \\1 & {- 1} & 1 & 1 \\{- 1} & 1 & 1 & 1\end{bmatrix}$ 13 $\begin{bmatrix}1 \\1 \\{- 1} \\1\end{bmatrix}\quad$ $\frac{1}{\sqrt{2}}\begin{bmatrix}1 & {- 1} \\1 & 1 \\{- 1} & 1 \\1 & 1\end{bmatrix}$ $\frac{1}{\sqrt{3}}\begin{bmatrix}1 & 1 & {- 1} \\1 & 1 & 1 \\{- 1} & 1 & 1 \\1 & {- 1} & 1\end{bmatrix}$ $\frac{1}{\sqrt{4}}\begin{bmatrix}1 & 1 & {- 1} & 1 \\1 & 1 & 1 & {- 1} \\{- 1} & 1 & 1 & 1 \\1 & {- 1} & 1 & 1\end{bmatrix}$ 14 $\begin{bmatrix}1 \\{- 1} \\1 \\1\end{bmatrix}\quad$ $\frac{1}{\sqrt{2}}\begin{bmatrix}1 & 1 \\{- 1} & 1 \\1 & 1 \\1 & {- 1}\end{bmatrix}$ $\frac{1}{\sqrt{3}}\begin{bmatrix}1 & {- 1} & 1 \\{- 1} & 1 & 1 \\1 & 1 & 1 \\1 & 1 & {- 1}\end{bmatrix}$ $\frac{1}{\sqrt{4}}\begin{bmatrix}1 & {- 1} & 1 & 1 \\{- 1} & 1 & 1 & 1 \\1 & 1 & 1 & {- 1} \\1 & 1 & {- 1} & 1\end{bmatrix}$ 15 $\begin{bmatrix}1 \\{- 1} \\{- 1} \\{- 1}\end{bmatrix}\quad$ $\frac{1}{\sqrt{2}}\begin{bmatrix}1 & {- 1} \\{- 1} & 1 \\{- 1} & {- 1} \\{- 1} & {- 1}\end{bmatrix}$ $\frac{1}{\sqrt{3}}\begin{bmatrix}1 & {- 1} & {- 1} \\{- 1} & 1 & {- 1} \\{- 1} & {- 1} & 1 \\{- 1} & {- 1} & {- 1}\end{bmatrix}$ $\frac{1}{\sqrt{4}}\begin{bmatrix}1 & {- 1} & {- 1} & {- 1} \\{- 1} & 1 & {- 1} & {- 1} \\{- 1} & {- 1} & 1 & {- 1} \\{- 1} & {- 1} & {- 1} & 1\end{bmatrix}$

indicates data missing or illegible when filed

<Closed-Loop MIMO>

A method of using a precoding weight similar to a channel according to achannel condition is called a closed-loop MIMO scheme. A method of usinga precoding weight according to a specific rule irrespective of achannel condition is called an open-loop MIMO scheme.

For the closed-loop MIMO scheme, the amount of the precoding weightreported by a receiver may vary according to a frequency unit, a reportcycle, and so on. The frequency unit may be defined as a frequency rangeto which one precoding weight is applied. System bandwidths may beclassified into frequency units, such as a wideband (WB), a subband(SB), and a bestband (BB) according to the frequency range. The subbandmay include at least one subcarrier, and the wideband may include atleast one subband. The bestband refers to a band having the best channelstate according to channel measurement in a receiver. In thecodebook-based precoding scheme, a defined PMI is fed back. A WB PMI, anSB PMI, and a BB PMI may be defined according to the range to which thePMI is applied. A PMI capable of maximizing the average throughput ofresources of a specific band is selected from among defined precodingmatrices. The precoding weight has better performance with a reductionin the range.

Assuming that a bundle of 12 consecutive subcarriers is called aresource block, the system bandwidth and the subband may be representedby using the resource block as a basic unit. Table 3 shows an example inwhich the system bandwidth and the subband are represented by using theresource block as the basic

TABLE 3 System bandwidth Subband size M (number of bestbands) 6-7Wideband CQI only Wideband CQI only  8-11 2 1 11-26 2 3 27-63 3 5 64-110 4 6

The wideband (WB) may be defined as a system bandwidth or as thegreatest unit for calculating a CQI. The subband (SB) may be defined asa k number of consecutive resource blocks and as a minimum unit forcalculating a CQI. The number of bestbands may be determined accordingto the system bandwidth.

Different subband sizes may be defined according to the systembandwidth. A CQI calculation range and a PMI application range may havethe same value. For example, in a system having 24 resource blocks asthe system bandwidth, a method of calculating a CQI and applying a PMIis described.

(1) In the case where a WB CQI and a WB PMI are transmitted, a receiverselects a PMI capable of maximizing the average throughput of the 24resource blocks and calculates an average CQI of the 24 resource blocksusing the selected PMI. The receiver can find one WB CQI and one WB PMI.

(2) In the case where an SB CQI and an SB PMI are transmitted, areceiver selects a PMI for subbands consisting of two resource blocksand calculates an average CQI. The receiver can find 12 SB CQIs and 12SB PMIs.

(3) In the case where an SB CQI and a WB PMI are transmitted, a receiverselects a PMI capable of maximizing the average throughput of the 24resource blocks and calculates an average CQI per two resource blocksusing the PMI (12 CQIs/1 PMI). The receiver can find 12 SB CQIs and oneWB PMI.

(4) In the case where a WB CQI and an SB PMI are transmitted, a receiverselects a PMI per two resource blocks and calculates an average CQI ofthe 24 resource blocks using the selected PMIs. The receiver can findone WB CQI and 12 SB PMIs.

(5) In the case where best M average CQI/PMI and WB CQI/PMI aretransmitted, a receiver selects 3 subbands having the best throughput,from among subbands of two resource block unit, selects a PMI for thebestband (2×3=6RB), calculates an average CQI of the bestbands, selectsa PMI for all the band 24 resource blocks, and calculates a CQI.

<Opportunistic Beamforming>

When taking scheduling in which resources are allocated to a user havingalmost the highest point in a channel condition into consideration, inthe case where the channel of each user is in a static channel conditionwhose change is slow, a multi-user diversity gain is reduced. A schemefor raising the multi-user gain by making the static channel conditioninto a faster and greater channel condition through spatial signalprocessing is called an opportunistic beamforming scheme. If theopportunistic beamforming scheme is used, a BS may have an effect offorming a beam in an irregular direction by using a precoding weighthaving the size and phase of an irregular form in each antenna.Accordingly, a channel condition of each user can be changed moredynamically. In this case, if both the opportunistic beamforming schemeand the scheduling scheme are used in a channel condition in which achannel slowly changes, a greater multi-user diversity gain can beobtained. Furthermore, in an OFDMA system, a different precoding weightmay be applied for every frequency resources. A scheduling gain may beobtained by making a frequency flat channel into a frequency selectivechannel. Frequency resources in an OFDMA system include a subblock, aresource block, subcarriers, and so on.

The codebook-based precoding scheme is a method of selecting a precodingmatrix which is the most similar to a channel condition, from amongpredetermined precoding matrices, and reporting a PMI. Thecodebook-based precoding scheme is advantageous in that it can reduceoverhead resulting from feedback data, but it has to configure acodebook using a combination of more codebook sets with an increase ofthe number of transmission antennas because the codebook consists of acombination of codebook sets which can represent spatial channels. Withan increase in the number of transmission antennas, there is adifficulty in designing the codebook. With an increase in the size ofthe codebook, the overhead of feedback data may be increased.

A method of applying the codebook-based precoding scheme to extendedtransmission antennas using the existing defined codebook is describedbelow.

FIG. 4 shows antenna clustering according to an embodiment of thepresent invention.

Referring to FIG. 4, in order to apply the codebook-based precodingscheme to extended transmission antennas, antenna clustering andchannel-dependent precoding are used. When precoding weights areconfigured for the codebook-based precoding of a transmitter havingextended antennas, some of the precoding weights may use thechannel-dependent precoding using the existing codebook and theremaining precoding weights may also use the channel-dependent precodingusing the existing codebook.

<Antenna Clustering and Channel-Dependent Precoding>

The antenna clustering is to configure a Z number of antenna clusters bybinding a P number of transmission antennas by N (P, N, and Z are aninteger greater than 0). The channel-dependent precoding may be appliedto each antenna cluster. For example, as shown, in 8Tx transmission, twoantenna clusters may be configured by binding four antennas. Thechannel-dependent precoding may be applied to each of the two antennaclusters.

The antenna cluster having an N number of the antennas can support 1 toN ranks. In each of the antenna clusters, a PMI representing a maximumthroughput may be selected by using the codebook of the ranks 1 to N andused.

Equation 9 shows a precoding weight matrix including a precoding weightW_(z)(i) having a layer whose size is V_(z) in a Z^(th) antenna clusterhaving a P_(z) number of transmission antennas.

$\begin{matrix}{{W(i)} = \begin{bmatrix}{W_{0}(i)} & 0 & \ldots & 0 \\0 & {W_{1}(i)} & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & {W_{Z - 1}(i)}\end{bmatrix}} & \left\lbrack {{Equation}\mspace{14mu} 9} \right\rbrack\end{matrix}$

wherein M(i) is a precoding weight P_(z)×V_(z) for the z^(th) antennacluster, P_(z) is the number of transmission antennas for the z^(th)antenna cluster, V_(z) is the number of layers for the Z^(th) antennacluster. W(i) is a Drecoding weight P×V matrix for the transmissionantenna,

number of transmission antennas

is the total number of layers and

${{\,^{P}V} = {\sum\limits_{{z = 0},\mspace{11mu} \ldots \mspace{14mu},{Z - 1}}V_{z}}},$

i=0,1, . . . , M_(symb) ^(layer)−1, and M_(symb) ^(layer) is the numberof modulation symbols per layer. The precoding weight for each antennacluster may be a precoding matrix previously defined in the existingsystem. For example, the precoding weight for each antenna cluster maybe the precoding matrix of a codebook for 4Tx or 2Tx transmission whichis defined in a 4Tx system.

In the z^(th) antenna cluster having a P_(z) number of the transmissionantennas, if the precoding weight W_(z)(i) having a layer having a sizeof V_(z) is selected, W_(z)(i) becomes a matrix of a P_(z)×V_(z) size.In order for a different rank to be transmitted in each antenna cluster,the precoding weight matrix of the antenna clusters has a block diagonalform. Accordingly, the precoding weight matrix used in a transmitter maybecome a matrix of a P×V size having a diagonal form. In the matrix ofthe block diagonal form, elements not 0 consist of (1,1), (2,2), (3,3)to (m,n) or (1,n), (2,n−1), (3,n-2) to (m,1) and mean matricesconsisting of elements of 0 in the remaining locations (wherein mindicates the location of a row and n indicates the location of acolumn, m and n are an integer greater than 0).

Equation 10 shows a signal generated by an antenna cluster.

$\begin{matrix}{{{Y(i)} = {{{W(i)}{X(i)}} = {\begin{bmatrix}{W_{0}(i)} & 0 & \ldots & 0 \\0 & {W_{1}(i)} & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & {W_{Z - 1}(i)}\end{bmatrix}\begin{bmatrix}{X_{0}(i)} \\{X_{1}(i)} \\\vdots \\{X_{Z - 1}(i)}\end{bmatrix}}}}\mspace{79mu} {{Y(i)} = \begin{bmatrix}{y^{(0)}(i)} & {y^{(1)}(i)} & \ldots & {y^{({P - 1})}(i)}\end{bmatrix}^{T}}\mspace{79mu} {{X_{z}(i)} = \begin{bmatrix}{x_{z}^{(0)}(i)} & {x_{z}^{(1)}(i)} & \ldots & {x_{z}^{({V_{z} - 1})}(i)}\end{bmatrix}^{T}}} & \left\lbrack {{Equation}\mspace{14mu} 10} \right\rbrack\end{matrix}$

The signal X_(z)(i) having the V_(z) layer of the z^(th) antenna clusteris inputted to the precoder. The precoder generates y^(P)(i) mapped tothe p^(th) antenna port. y^(P)(i) may be represented by a vector columnY(i).

The precoding weight matrix W(i) for two antenna clusters may berepresented by Equation 11.

$\begin{matrix}{{W(i)} = \begin{bmatrix}{W_{0}(i)} & 0 \\0 & {W_{1}(i)}\end{bmatrix}} & \left\lbrack {{Equation}\mspace{14mu} 11} \right\rbrack\end{matrix}$

For example, assuming a system in which four antennas are bound to formtwo antenna clusters in 8Tx transmission, precoding weights used in thefirst antenna cluster and the second antenna cluster enable transmissionof the ranks 1 to 4. A rank combination of the antenna clusters may be(1,1), (1,2), (1,3), (1,4), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2),(3,3), (3,4), (4,1), (4,2), (4,3), and (4,4). In order to performdifferent rank transmission in the two antenna clusters, the precodingweight matrix of a diagonal form is appropriate.

Equation 12 shows a case where a diagonal matrix D(k_(i)) for CyclicDelay Diversity (CDD) is applied in the precoding weight matrix.

$\begin{matrix}{{{D\left( k_{i} \right)}{W(i)}} = {\begin{bmatrix}\theta_{0} & 0 & \ldots & 0 \\0 & \theta_{1} & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & \theta_{P - 1}\end{bmatrix}{W(i)}}} & \left\lbrack {{Equation}\mspace{14mu} 12} \right\rbrack\end{matrix}$

wherein θ_(p)=−2π·k_(i)·p·δ, p=0, . . . , P−1, and k_(i) is thefrequency domain index of a resource element to which a complex valuesymbol y(i) is mapped. A phase θ_(p) is increased according to anincrease of a frequency index k₁ and a transmission antenna index p, anda delay value δ may be defined as in Table 4.

TABLE 4 2Tx 4Tx 8Tx 1 2/η 1/η — 2 4/η 2/η 1/η η = {128, 256, 512, 1024,2048}

wherein η may have the same value as the FFT size of a system bandwidthor fixedly one of five values irrespective of a system bandwidth.

The diversity diagonal matrix D(i) may be represented by a combinationof D_(z)(i) defined for each antenna cluster and may be represented byEquation 13.

$\begin{matrix}{{{D(i)}{W(i)}} = {\begin{bmatrix}{D_{0}(i)} & 0 & \ldots & 0 \\0 & {D_{1}(i)} & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & {D_{Z - 1}(i)}\end{bmatrix}{\quad{{\begin{bmatrix}{W_{0}(i)} & 0 & \ldots & 0 \\0 & {W_{1}(i)} & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & {W_{Z - 1}(i)}\end{bmatrix}\mspace{79mu} {D_{z}(i)}} = \left\lbrack \begin{matrix}\theta_{0} & 0 & \ldots & 0 \\0 & \theta_{1} & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & \theta_{P - 1}\end{matrix} \right\rbrack}}}} & \left\lbrack {{Equation}\mspace{14mu} 13} \right\rbrack\end{matrix}$

wherein θ_(p)=−2π·k_(i)·p·δ, p=0, . . . , P_(x)−1

The delay diagonal matrix D_(z)(i) and a Discrete Fourier Transform(DFT) unitary matrix U_(z) for each antenna cluster may be defined usinga precoding spatial multiplex (SM) scheme using wide delay CDD.

Equation 14 shows a case where the DFT unitary matrix U_(z) is appliedto a precoding weight matrix.

$\begin{matrix}{{{W(i)}{D(i)}U} = {\quad{\begin{bmatrix}{W_{0}(i)} & 0 & \ldots & 0 \\0 & {W_{1}(i)} & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & {W_{Z - 1}(i)}\end{bmatrix}{\quad{{{\begin{bmatrix}{D_{0}(i)} & 0 & \ldots & 0 \\0 & {D_{1}(i)} & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & {D_{Z - 1}(i)}\end{bmatrix}\begin{bmatrix}U_{0} & 0 & \ldots & 0 \\0 & U_{1} & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & U_{Z - 1}\end{bmatrix}}\mspace{79mu} {D_{z}(i)}} = {{\begin{bmatrix}1 & 0 & \ldots & 0 \\0 & ^{{- {j2}}\; {m/V_{z}}} & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & ^{{- {j{({V_{z} - 1})}}}2\; {m/V_{z}}}\end{bmatrix}\mspace{79mu} U_{z}} = {DFT}_{V_{z}}}}}}}} & \left\lbrack {{Equation}\mspace{14mu} 14} \right\rbrack\end{matrix}$

wherein V_(z) is the number of layers of the z^(th) antenna cluster, andthe sizes of D_(z)(i) and U_(z) may be determined according to thenumber of layers V_(z) of the z^(th)antenna cluster. The precodingmatrix W_(z)(i) of the z^(th) antenna cluster may be circularly selectedaccording to the frequency index.

The sizes of the delay diagonal matrix D(i) and the unitary DFT matrix Umay be determined by the sum of layers transmitted from antenna clustersand may be represented by Equation 15.

$\begin{matrix}{{{{W(i)}{D(i)}U} = {\begin{bmatrix}{W_{0}(i)} & 0 & \ldots & 0 \\0 & {W_{1}(i)} & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & {W_{2 - 1}(i)}\end{bmatrix}{D(i)}U}}{{D(i)} = \begin{bmatrix}1 & 0 & \ldots & 0 \\0 & ^{{- {j2}}\; {{\pi }/V}} & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & ^{{- j}\; {({V - 1})}2\pi \; {/V}}\end{bmatrix}}{U = {DFT}_{V}}} & \left\lbrack {{Equation}\mspace{14mu} 15} \right\rbrack\end{matrix}$

wherein V is the total number of layers, and the precoding matrixW_(z)(i) may be circularly selected according to the frequency index asin Equation 14.

Physical antennas to which antenna clusters are mapped may be selectedusing an antenna switching matrix. They may be represented by Equation16.

AW(i)   [Equation 16]

wherein A is the antenna switching matrix P×P, and W(i) is the precodingmatrix P×V.

The antenna switching matrix may produce a P! type of a matrix. Forexample, assuming a system having 8Tx, the type of the antenna switchingmatrix may become 8! so that the precoding weight is mapped to thephysical antenna.

Equation 17 shows an example of physical antenna switching matrices A₀to A₃ to which the precoding weight is mapped.

$\begin{matrix}{{A_{0} = \begin{bmatrix}1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\end{bmatrix}}{A_{1} = \begin{bmatrix}1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\end{bmatrix}}{A_{2} = \begin{bmatrix}0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 1 & 0 & 0 & 0 & 0\end{bmatrix}}{A_{3} = \begin{bmatrix}0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\0 & 0 & 0 & 1 & 0 & 0 & 0 & 0\end{bmatrix}}} & \left\lbrack {{Equation}\mspace{14mu} 17} \right\rbrack\end{matrix}$

The physical antenna switching matrices A₀ to A₃ indicate the physicalantennas to which the precoding weight is mapped. Accordingly, thenumbers of mapped physical antennas may be represented as in Table 5.

TABLE 5 Antenna Cluster #1 Antenna Cluster #2 A₀ 1, 2, 3, 4 5, 6, 7, 8A₁ 1, 3, 5, 7 2, 4, 6, 8 A₂ 5, 6, 7, 8 1, 2, 3, 4 A₃ 2, 4, 6, 8 1, 3, 5,7

In the case of A₀, the antenna cluster #1 is mapped to the 1, 2, 3, and4^(th) antennas, and the antenna cluster #2 is mapped to the 5, 6, 7,and 8^(th) antennas. In the case of A₁, the antenna cluster #1 is mappedto 1, 3, 5, and 7^(th) antennas, and the antenna cluster #2 is mapped to2, 4, 6, and 8^(th) antennas. A₂ and A₃ have a swapping relationshipwith A₀ and A₁, respectively.

Equation 18 may be represented by combining Equations 12, 13, and 16.

AD(i)W(i)   [Equation 18]

The location of an antenna clustered from among all the P antennas isdetermined by a matrix A.

Equation 19 may be represented by combining Equations 14, 15, and 16.

AW(i)D(i)U   [Equation 19]

The location of an antenna clustered from among all the P antennas isdetermined by a matrix A.

Equation 20 represents the data of each antenna cluster in rank 1transmission.

X ₀(i)=X ₁(i)= . . . =X _(Z−1)(i)   [Equation 20]

V_(z)=1

z=0, . . , Z−1

In rank 1 transmission, the number of layers of all the antenna clustersis 1, and the same data is transmitted. A Z number of PMIs for a Znumber of antenna clusters and one CQI are required as feedback data.

Equation 21 shows an example of data in which the precoding weight isapplied to two antenna clusters having 4Tx antennas in 8Tx transmission.

$\begin{matrix}{{{{W(i)}{X(i)}} = {\begin{bmatrix}{W_{00}(i)} & 0 \\{W_{01}(i)} & 0 \\{W_{02}(i)} & 0 \\{W_{03}(i)} & 0 \\0 & {W_{10}(i)} \\0 & {W_{11}(i)} \\0 & {W_{12}(i)} \\0 & {W_{13}(i)}\end{bmatrix}\begin{bmatrix}{X_{0}(i)} \\{X_{1}(i)}\end{bmatrix}}},{{X_{0}(i)} = {X_{1}(i)}}} & \left\lbrack {{Equation}\mspace{14mu} 21} \right\rbrack\end{matrix}$

Assuming two antenna clusters having 4Tx in 8Tx transmission, a PMI foreach of the two antenna clusters is selected every antenna cluster. Aweight capable of maximizing the throughput of 8Tx rank 1 transmissionis selected as the two PMIs.

The throughput may be calculated on the basis of the SNR. The SNR may becalculated as in Equation 22.

$\begin{matrix}{{\begin{matrix}{{HW} = {\begin{bmatrix}{\hat{H}}_{0} & {\hat{H}}_{1}\end{bmatrix}\begin{bmatrix}{\hat{W}}_{0} & 0_{4 \times 1} \\0_{4 \times 1} & {\hat{W}}_{1}\end{bmatrix}}} \\{= \begin{bmatrix}{{\hat{H}}_{0}{\hat{W}}_{0}} & 0 \\0 & {{\hat{H}}_{1}{\hat{W}}_{1}}\end{bmatrix}} \\{= \begin{bmatrix}{\overset{\sim}{H}}_{0} & 0 \\0 & {\overset{\sim}{H}}_{1}\end{bmatrix}}\end{matrix}{{SNR} = \frac{{{\overset{\sim}{H}}_{0}}^{2} + {{\overset{\sim}{H}}_{1}}^{2}}{\sigma^{2}}}{{\hat{H}}_{0} = \begin{bmatrix}H_{0} & H_{1} & H_{2} & H_{3}\end{bmatrix}},{{\hat{H}}_{1} = \begin{bmatrix}H_{4} & H_{5} & H_{6} & H_{7}\end{bmatrix}}}{{{\hat{W}}_{0} = \begin{bmatrix}W_{00} & W_{01} & W_{02} & W_{03}\end{bmatrix}^{T}},{{\hat{W}}_{1} = \begin{bmatrix}W_{10} & W_{11} & W_{12} & W_{13}\end{bmatrix}^{T}}}{{\overset{\sim}{H}}_{0} = {{H_{0}W_{00}} + {H_{1}W_{01}} + {H_{2}W_{02}} + {H_{3}W_{03}}}}{{\overset{\sim}{H}}_{1} = {{H_{4}W_{10}} + {H_{5}W_{11}} + {H_{6}W_{12}} + {H_{7}W_{13}}}}} & \left\lbrack {{Equation}\mspace{14mu} 22} \right\rbrack\end{matrix}$

Here, when the antenna clusters have the same number of layers, theprecoding weight matrix may be represented by Equation below.

$\begin{matrix}{{W(i)} = \begin{bmatrix}{a\; {W_{0}(i)}} & {b\; {W_{1}(i)}} \\{c\; {W_{2}(i)}} & {d\; {W_{3}(i)}}\end{bmatrix}} & \left\lbrack {{Equation}\mspace{14mu} 23} \right\rbrack\end{matrix}$

wherein a, b, c, and d are weight factors for configuring the precodingweight matrix in various ways. The weight factor may be a specificcomplex scalar value. In order to simplify the precoding operation, theweight factor may be limitedly used. A codebook may be configured to apredetermined weight factor. For example, the weight factor may be

${\frac{{\pm 1} \pm j}{\sqrt{2}}{sing}},{\pm 1},$

and ±j of ±1, ±j or 8PSK of QPSK. Accordingly, finally, the codebookW(i) may consist of the weight factor of QPSK or 8PSK. W(i) may beconfigured as in W(i)W^(H)(i)=W^(H)(i)=I. The weight factor may have adetermined value so that it is power normalized.

Some of the precoding weight matrices may be the same. For example, theprecoding weight matrices may be configured as W₀(i)=W₁(i), W₂(i)=W₃(i)or W₀(i)=W₂(I), W₁(i)=W₃(i).

Equation 24 represents a precoding weight matrix when a=1, b=1, c=1,d=−1, and W0(i)=W1(i), W2(i)=W3(i).

$\begin{matrix}{{W(i)} = \begin{bmatrix}{W_{0}(i)} & {W_{0}(i)} \\{\; {W_{1}(i)}} & {- {W_{1}(i)}}\end{bmatrix}} & \left\lbrack {{Equation}\mspace{14mu} 24} \right\rbrack\end{matrix}$

Equation 25 represents a precoding weight matrix when a=1, b=1, c=1, andd=−1 and W₀(i)=W₂(i), W₁(i)=W₃(i).

$\begin{matrix}{{W(i)} = \begin{bmatrix}{W_{0}(i)} & {W_{1}(i)} \\{\; {W_{0}(i)}} & {- {W_{1}(i)}}\end{bmatrix}} & \left\lbrack {{Equation}\mspace{14mu} 25} \right\rbrack\end{matrix}$

Equation 26 represents a precoding weight matrix when a=1, b=1, c=j, andd=−j and W₀(i)=W₁(i), W₂(i)=W₃(i).

$\begin{matrix}{{W(i)} = \begin{bmatrix}{W_{0}(i)} & {W_{0}(i)} \\{\; {j\; {W_{1}(i)}}} & {{- j}\; {W_{1}(i)}}\end{bmatrix}} & \left\lbrack {{Equation}\mspace{14mu} 26} \right\rbrack\end{matrix}$

Equation 27 represents a precoding weight matrix when a=1, b=1, c=j, andd=−−j and W₀(i)=W₂(i), W₁(i)=W₃(i).

$\begin{matrix}{{W(i)} = \begin{bmatrix}{W_{0}(i)} & {W_{1}(i)} \\{\; {j\; {W_{0}(i)}}} & {{- j}\; {W_{1}(i)}}\end{bmatrix}} & \left\lbrack {{Equation}\mspace{14mu} 27} \right\rbrack\end{matrix}$

Equation 28 represents a precoding weight matrix when a=1, b=j, c=1, andd=−j and W₀(i)=W₁(i), W₂(i)=W₃(i).

$\begin{matrix}{{W(i)} = \begin{bmatrix}{W_{0}(i)} & {j\; {W_{0}(i)}} \\{\; {W_{1}(i)}} & {{- j}\; {W_{1}(i)}}\end{bmatrix}} & \left\lbrack {{Equation}\mspace{14mu} 28} \right\rbrack\end{matrix}$

Equation 29 represents a precoding weight matrix when a=1, b=j, c=1, andd=−j and W₀(i)=W₂(i), W₁(i)=W₃(i).

$\begin{matrix}{{W(i)} = \begin{bmatrix}{W_{0}(i)} & {j\; {W_{1}(i)}} \\{\; {W_{0}(i)}} & {{- j}\; {W_{1}(i)}}\end{bmatrix}} & \left\lbrack {{Equation}\mspace{14mu} 29} \right\rbrack\end{matrix}$

Some of the precoding weight matrices may become complex-conjugated.Equation 30 to 33 shows an example of a complex conjugated precodingweight matrix.

$\begin{matrix}{{W(i)} = {\begin{bmatrix}{W_{0}(i)} & 0 \\{\; 0} & {W_{1}(i)}\end{bmatrix}\begin{bmatrix}I & I \\I & {- I}\end{bmatrix}}} & \left\lbrack {{Equation}\mspace{14mu} 30} \right\rbrack \\{{W(i)} = {\begin{bmatrix}{W_{0}(i)} & 0 \\{\; 0} & {W_{1}(i)}\end{bmatrix}\begin{bmatrix}{a\; I} & {b\; I} \\{c\; I} & {d\; I}\end{bmatrix}}} & \left\lbrack {{Equation}\mspace{14mu} 31} \right\rbrack \\{{W(i)} = {\begin{bmatrix}I & I \\I & {- I}\end{bmatrix}\begin{bmatrix}{W_{0}(i)} & 0 \\{\; 0} & {W_{1}(i)}\end{bmatrix}}} & \left\lbrack {{Equation}\mspace{14mu} 32} \right\rbrack \\{{W(i)} = {\begin{bmatrix}{a\; I} & {b\; I} \\{c\; I} & {d\; I}\end{bmatrix}\begin{bmatrix}{W_{0}(i)} & 0 \\{\; 0} & {W_{1}(i)}\end{bmatrix}}} & \left\lbrack {{Equation}\mspace{14mu} 33} \right\rbrack\end{matrix}$

A diagonal matrix D(i) and/or a DFT unitary matrix U(i) for CDD may beapplied to the complex conjugated precoding weight matrix. Equation 34to 36 show examples in which the diagonal matrix D(i) is applied to thecomplex conjugated precoding weight matrix.

$\begin{matrix}{{W(i)} = {\begin{bmatrix}{W_{0}(i)} & 0 \\{\; 0} & {W_{1}(i)}\end{bmatrix}{{D(i)}\begin{bmatrix}I & I \\I & {- I}\end{bmatrix}}}} & \left\lbrack {{Equation}\mspace{14mu} 34} \right\rbrack \\{{W(i)} = {\begin{bmatrix}{W_{0}(i)} & 0 \\{\; 0} & {W_{1}(i)}\end{bmatrix}{{D(i)}\begin{bmatrix}{a\; I} & {b\; I} \\{c\; I} & {d\; I}\end{bmatrix}}}} & \left\lbrack {{Equation}\mspace{14mu} 35} \right\rbrack \\{{W(i)} = {\begin{bmatrix}{a\; {W_{0}(i)}} & {b\; {W_{1}(i)}} \\{\; {c\; {W_{2}(i)}}} & {d\; {W_{3}(i)}}\end{bmatrix}{D(i)}}} & \left\lbrack {{Equation}\mspace{14mu} 36} \right\rbrack\end{matrix}$

Equation 37 shows an example in which the DFT unitary matrix is appliedto the complex conjugated precoding weight matrix.

$\begin{matrix}{{{W(i)} = {\begin{bmatrix}{W_{0}(i)} & 0 \\{\; 0} & {W_{1}(i)}\end{bmatrix}\left\lbrack {U(i)} \right\rbrack}}{{U(i)} = {I \otimes {W_{2}(i)}}}} & \left\lbrack {{Equation}\mspace{14mu} 37} \right\rbrack\end{matrix}$

wherein W₂(i) is a unitary matrix.

Equation 38 shows an example in which the diagonal matrix D(i) and theDFT unitary matrix U(i) are applied to the complex conjugated precodingweight matrix.

$\begin{matrix}{{W(i)} = {\begin{bmatrix}{W_{0}(i)} & 0 \\{\; 0} & {W_{1}(i)}\end{bmatrix}{{D(i)}\left\lbrack {U(i)} \right\rbrack}}} & \left\lbrack {{Equation}\mspace{14mu} 38} \right\rbrack\end{matrix}$

The complex conjugated precoding weight matrix and the unitary matrixmay be represented by Equation 39.

$\begin{matrix}{{{W()} = \left\{ {{\frac{1}{2}\begin{bmatrix}{W_{0}()} & {W_{0}()} \\{W_{1}()} & {- {W_{1}()}}\end{bmatrix}},{\frac{1}{2}\begin{bmatrix}{W_{0}()} & {W_{0}()} \\{j\; {W_{1}()}} & {{- j}\; {W_{1}()}}\end{bmatrix}}} \right\}}\mspace{20mu} {{W_{2}()} = \left\{ {{\frac{1}{2}\begin{bmatrix}1 & 1 \\1 & {- 1}\end{bmatrix}},{\frac{1}{2}\begin{bmatrix}1 & 1 \\j & {- j}\end{bmatrix}}} \right\}}} & \left\lbrack {{Equation}\mspace{14mu} 39} \right\rbrack\end{matrix}$

The complex conjugated precoding weight matrix may be represented byEquation 40.

$\begin{matrix}{{W()} = \begin{bmatrix}{W_{0}()} \\{W_{1}()}\end{bmatrix}} & \left\lbrack {{Equation}\mspace{14mu} 40} \right\rbrack\end{matrix}$

If the weight factor of a complex scalar value is applied, the precodingweight matrix may be represented by Equation 41. In order to simplifythe precoding operation, the weight factor may be predetermined.

$\begin{matrix}{{W()} = \begin{bmatrix}{{aW}_{0}()} \\{{bW}_{1}()}\end{bmatrix}} & \left\lbrack {{Equation}\mspace{14mu} 41} \right\rbrack\end{matrix}$

W₁(i) may be W₀(i). Accordingly, the complex conjugated precoding weightmatrix may be represented by Equation 42.

$\begin{matrix}{{W()} = \begin{bmatrix}{{aW}_{0}()} \\{{bW}_{0}()}\end{bmatrix}} & \left\lbrack {{Equation}\mspace{14mu} 42} \right\rbrack\end{matrix}$

Assuming that a=1, b=1 and W₀(i)=W₁(i), the complex conjugated precodingweight matrix may be represented by Equation 43.

$\begin{matrix}{{W()} = \begin{bmatrix}{W_{0}()} \\{W_{0}()}\end{bmatrix}} & \left\lbrack {{Equation}\mspace{14mu} 43} \right\rbrack\end{matrix}$

Assuming that a=1, b=−1 and W₀(i)=W₁(i), the complex conjugatedprecoding weight matrix may be represented by Equation 44.

$\begin{matrix}{{W()} = \begin{bmatrix}{W_{0}()} \\{- {W_{0}()}}\end{bmatrix}} & \left\lbrack {{Equation}\mspace{14mu} 44} \right\rbrack\end{matrix}$

Assuming that a=1, b=j and W₀(i)=W₁(i), the complex conjugated precodingweight matrix may be represented by Equation 45.

$\begin{matrix}{{W()} = \begin{bmatrix}{W_{0}()} \\{j\; {W_{0}()}}\end{bmatrix}} & \left\lbrack {{Equation}\mspace{14mu} 45} \right\rbrack\end{matrix}$

Assuming that a=1, b=−j and W₀(i)=W₁(i), the complex conjugatedprecoding weight matrix may be represented by Equation 46.

$\begin{matrix}{{W()} = \begin{bmatrix}{W_{0}()} \\{{- j}\; {W_{0}()}}\end{bmatrix}} & \left\lbrack {{Equation}\mspace{14mu} 46} \right\rbrack\end{matrix}$

The precoding weight matrix and the unitary matrix may be represented byEquation 47.

$\begin{matrix}{{{W()} = \left\{ {{\frac{1}{\sqrt{2}}\begin{bmatrix}{W_{0}()} \\{W_{1}()}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}{W_{0}()} \\{- {W_{1}()}}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}{W_{0}()} \\{j\; {W_{1}()}}\end{bmatrix}},\mspace{20mu} {\frac{1}{\sqrt{2}}\begin{bmatrix}{W_{0}()} \\{{- j}\; {W_{1}()}}\end{bmatrix}},} \right\}}{{W_{2}()} = \left\{ {{\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\1\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\{- 1}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\j\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\{- j}\end{bmatrix}}} \right\}}} & \left\lbrack {{Equation}\mspace{14mu} 47} \right\rbrack\end{matrix}$

In at least one of Equations 24 to 47, W₀(i) and W₁(i) may beW₀(i)=W₁(i). Accordingly, an indicator to indicate W₀(i) or W₁(i) asfeedback information may be used. Here, the complex conjugated precodingweight matrix of Equation 39 may be represented by Equation 48.

W(i)=W ₀(i)I _(n) I _(n)

W ₂(i)=W ₀(i)

W ₂(i)   [Equation 48]

As described above, since the multiple extended antennas of an advancedsystem can be supported using the existing codebook, the complexity ofthe system can be reduced. Furthermore, the existing codebook can beused for the UEs of the existing system not supporting multiple extendedantennas, and backward compatibility for the existing system can beguaranteed. A UE may operate in a multiple antenna system, estimate aplurality of transmission antenna channels of a BS, feed achannel-dependent precoding matrix or PMI for a first cluster and asecond cluster, each including a plurality of different antennas, fromthe estimated channels back to the BS, and receive precoded andtransmitted data using a feedback precoding matrix or a precoding weightinduced from a PMI or directly used.

All the above functions may be executed by a processor, such as amicroprocessor, a controller, a microcontroller, an Application SpecificIntegrated Circuit (ASIC) according to software or program codes codedto perform the above functions. The design, development, andimplementation of the codes may be said to be evident to a person havingordinary skill in the art on the basis of the description of the presentinvention.

Although the embodiments of the present invention have been describedabove, those having ordinary skill in the art will appreciate that thepresent invention may be modified in various ways without departing fromthe technical spirit and scope of the present invention. Accordingly, itmay be said that the present invention is not limited to the embodimentsand includes all embodiments falling within the scope of the claims.

1-9. (canceled)
 10. A method for transmitting a signal in a multipleantenna system, the method performed by a transmitter and comprising:pre-coding the signal based on a codebook comprising first pre-codingmatrices; and transmitting the pre-coded signal using a radio resource,wherein each of the first pre-coding matrices is decomposed into adiagonal matrix and a unitary matrix, wherein the diagonal matrixcomprises a second pre-coding matrix as a diagonal entry, and whereinthe unitary matrix is configured in a form of $\begin{bmatrix}1 & 1 \\1 & {- 1}\end{bmatrix}\mspace{14mu} {{{or}\mspace{14mu}\begin{bmatrix}1 & 1 \\j & {- j}\end{bmatrix}}.}$
 11. The method of claim 10, wherein: each of the firstpre-coding matrices is for a first number of antennas grouped intoantenna clusters; the second pre-coding matrix has a second number ofrows; and a number of antennas belonging to one of the antenna clustersis set to the second number.
 12. The method of claim 11, wherein thefirst number is greater than the second number.
 13. The method of claim10, wherein the unitary matrix comprises a weight factor that isdetermined such that a transmit power of each antenna is normalized. 14.The method of claim 10, wherein: the diagonal matrix is configured in aform of $\begin{bmatrix}{W_{0}()} & 0 \\0 & {W_{0}()}\end{bmatrix};$ and W₀(i) denotes the second pre-coding matrix and idenotes an index for the radio resource.
 15. The method of claim 10,wherein: the diagonal matrix further comprises a third pre-coding matrixas a diagonal entry; the diagonal matrix is configured in a form of$\begin{bmatrix}{W_{0}()} & 0 \\0 & {W_{1}()}\end{bmatrix};$ and W₀(i) denotes the second pre-coding matrix, W₁(i)denotes the third pre-coding matrix, and i denotes an index for theradio resource.
 16. The method of claim 10, wherein the radio resourcecomprises at least one Orthogonal Frequency Division Multiplexing (OFDM)symbol.
 17. A transmitter comprising: a pre-coder for pre-coding asignal based on a codebook comprising first pre-coding matrices; and atransmitter for transmitting the pre-coded signal using a radioresource, wherein each of the first pre-coding matrices is decomposedinto a diagonal matrix and a unitary matrix, wherein the diagonal matrixcomprises a second pre-coding matrix as a diagonal entry, and whereinthe unitary matrix is configured in a form of $\begin{bmatrix}1 & 1 \\1 & {- 1}\end{bmatrix}\mspace{14mu} {{{or}\mspace{14mu}\begin{bmatrix}1 & 1 \\j & {- j}\end{bmatrix}}.}$
 18. The transmitter of claim 17, wherein: each of thefirst pre-coding matrices is for a first number of antennas grouped intoantenna clusters; the second pre-coding matrix has a second number ofrows; and a number of antennas belonging to one of the antenna clustersis set to the second number.
 19. The transmitter of claim 18, whereinthe first number is greater than the second number.
 20. The transmitterof claim 17, wherein the unitary matrix comprises a weight factor thatis determined such that a transmit power of a first number of antennasis normalized.
 21. The transmitter of claim 17, wherein: the diagonalmatrix is configured in a form of $\begin{bmatrix}{W_{0}()} & 0 \\0 & {W_{0}()}\end{bmatrix};$ and w₀(i) denotes the second pre-coding matrix, w₁(i)denotes an index for the radio resource.
 22. The transmitter of claim17, wherein: the diagonal matrix further comprises a third pre-codingmatrix as a diagonal entry; the diagonal matrix is configured in a formof $\begin{bmatrix}{W_{0}()} & 0 \\0 & {W_{1}()}\end{bmatrix};$ and W₀(i) denotes the second pre-coding matrix, W₁(9denotes the third pre-coding matrix, and i denotes an index for theradio resource.
 23. The transmitter of claim 17, wherein the radioresource comprises at least one Orthogonal Frequency DivisionMultiplexing (OFDM) symbol.